1. Technical Field of the Invention
The present invention generally relates to integrated circuit digital filter structures and, more particularly, to a multiplexed FIR/IIR digital filter structure.
2. Description of Related Art
A fundamental building block in the field of digital signal processing is the digital filter. As is elementary in this field, digital filters refer to the filtering of sampled-data or discrete-time signals which are typically digital representations of analog signals which have been generated by way of analog-to-digital conversion. Fundamentally, a digital filter is a computational process, carried out either through dedicated hardware or through the execution of a sequence of instructions by programmable logic, by way of which an input sequence of numbers is converted into an output sequence of numbers, modified by a transfer function. Typical transfer functions refer to the frequency characteristics of the filter; analogously to analog filter counterparts, examples of digital filter transfer functions include low-pass, high-pass, band-pass, etc. Digital filter computations typically include digital addition, digital multiplication of signal values by constants, and the insertion of delay stages.
As is also well known in the art, digital filters are often classified according to their impulse response. Finite impulse response (FIR) digital filters refer to the class of filters in which only a finite number of input samples affect the generation of a given output sample; typically, FIR digital filters perform computations upon a finite number of input samples (i.e., the current sample, and a selected number of preceding input samples), in a non-recursive fashion. Infinite impulse response (IIR) digital filters are a class of filters in which previous output samples are also used in generating a current output sample, and are thus typically realized in a recursive fashion, including feedback of output sample values. Because of the feedback of prior output values, each current output value of an IIR filter depends upon the value of an infinite series of input sample values, hence the term “infinite impulse response”.
Due to their high computation efficiency, both FIR and IIR halfband (HB) digital filters are widely employed in Sigma-Delta A/D and D/A converters to perform decimation/interpolation functions. A cascade of a number of HB filters can be used to filter and decimate oversampled 1-bit or mutli-bit signals by a factor of power-of-two number in Sigma-Delta A/D converters for example. The interpolation function is performed in Sigma-Delta D/A converters.
Because of their linear phase response, FIR HB filters have been more frequently employed eventhough the higher computational complexity of FIR HB filters requires larger silicon area than that of their IIR counterparts. FIR HB filters also have a relatively long group delay. In a cascade of several FIR HB filters for decimation purpose the dominant group delay lies in the last stage, which usually is a very high-order filter because of narrow transition band need. Since the group delay of an FIR HB filter is proportional to its order, the delay cannot be effectively reduced without lowering the filter performance.
One disadvantage with IIR digital filters is due to a well-known problem referred to as “limit cycles”. The limit cycle problem is manifest in digital filters that generate a self oscillating behavior caused by nonlinearity of quantizers. One example of this limit cycle behavior is the response of a filter when the input of the filter is reduced to zero. Rounding errors caused by the use of finite precision arithmetic mean that the output of the filter does not necessarily reduce to zero when the input reduces to zero. Instead, the output can stay at a non-zero value or oscillate about zero. Although it is well known to use magnitude truncation as the quantization approach to reduce the zero-input limit cycles in a first-order IIR filter, this approach is very complex and can be very expensive.
A new approach is desirable for applications in which lower filter performance is not an option and low group delay is desired, particularly for high speed sample rates (i.e., 250 kHz and higher).